Nick Paul also scored for Ottawa (2-1-0), while Connor Brown's three assists gave him 100 career helpers. Ottawa remains undefeated on home ice after two games (2-0-0).
Filip Gustavsson made 32 saves in his first regular-season NHL game since May 12.
Michael Raffl and Joe Pavelski scored for the Stars (1-2-0).
Anton Khudobin, who stopped 24 shots, suffered his first regulation loss against the Senators. Coming in, the Stars netminder was 8-0-2 against Ottawa.
Trailing 3-1, the Stars pushed back in the third. Pavelski was able to pick up a loose puck in front off a Radek Faksa rebound to make things interesting, but couldn't complete the comeback.
Ottawa scored two power-play goals in the second to take a 3-1 lead but finished the period without Tim Stutzle. He returned to start the third.
Tierney picked up his first of the night as a Shane Pinto shot deflected off his chest at 9:20 of the second, and with one minute remaining in the period he took a pass from Zach Sanford and pushed the puck towards the net to beat Khudobin.
Of concern was a slash to Stutzle's left wrist by Faksa that went uncalled. The 19-year-old left the ice hunched over in pain clutching his wrist.
The two teams exchanged goals in the first to make it 1-1.
The Stars scored on their first shot as Raffl had room in front and buried a feed from Alexander Radulov. Less than a minute later Paul tucked a backhander under the crossbar.
This marked the first American-based opponent to visit Canadian Tire Centre since March 5, 2020.
Notes: Brady Tkachuk did not play Sunday, but will likely make his season debut Thursday for the Senators. ... Scott Sabourin and Victor Mete were healthy scratches for Ottawa. ... Stars defenceman John Klingberg missed his second straight game with a lower-body injury suffered in the team's season opener.